Daily Tasks has a database of all known Task Bulletin Boards and the Tasks that they contain. It can not only list these, but can also check your inventory for trophy items and show which items can be turned in to complete tasks (and if one of your alts can use it).

You can also list which trophy items can't be used and can check on individual trophy items. You can even display which items in your inventory can be used by a player of a specified level.

New with version 2, you can now check which mobs drop an item or what items a mob drops (the mob list is still a work-in-progress).

Basic commands:
/dt (Lists all trophy items in inventory and their uses)
/dtu (Lists all trophy items in inventory that are usable)
/dtc (Lists all trophy items in inventory that can complete a task)
/dtx (Lists all trophy items in inventory that are unusable)
/dtj (Lists all trophy items in inventory that are junk)
/dtv (Lists all trophy items in vault and their uses)
/dts (Lists all trophy items in shared storage and their uses)
/dtd (Lists items in shared storage that duplicate bag items)
/dtl (Lists task locations)
/dlz (Lists task zones)
/dtm (lists mobs and what trophies they drop)
/dtp (Lists known player characters)
/dtp <name> (Deletes player name)
/dtr (Lists reputation codes)
/dtr list (Lists alt chars with kindred rep codes)
/dtb (Move listed items to selected bag)
/dtw (Opens a windowed version of DT)

I received a bug report for Haerondir not listing any trophies. It's fixed in the next version but until I post a new version you can apply the fix by adding '--' to the start of line #145 "the Wastes" in DT_Data.lua.

Is it possible to make that listing the vault/shared items also respect the char/complete/location filter?

Yes, but the way that it is currently coded, it will take a lot of work. It's one of the things on my "to do when I have a lot of extra time" list. Another item on that list is to create a structured output window instead of sending everything to chat. I'd also like to add a general-purpose structured help facility to all my addons, but there are many other things that I want to spend time on like my new 3D printer and CNC router.

So I'll add a +1 to the priority of your request but I can't say when it might get implemented.

This is just a cosmetic update. I changed the rep. code "DM" to "MT" so that it would better match the task board listings and be easier to recognize.

I also enhanced the listing of rep codes by adding the highest level character name that could increase that reputation. I mainly added this so that it would be easier to see which alt to give rep. items to.

This version includes the typo fix for "Stone-worn Fur", but it also includes the first functional enhancement in 3 years! Read on for details.

I use the "Find top rep item uses" feature a lot to decide which alt I should pass trophies to for increasing reputation. At one time, you had to have kindred reputation before you could buy Return/Guide/Muster skills, so the kindred rep setting was a good way to decide when to pass on rep items. However, rep requirements have been dropping with game updates and in recent updates, you can get skills with as little as an acquaintance rep. This has led to many cases where I've gotten the desired skill and want to pass on rep trophies but don't have kindred rep yet, so the "Find top" button doesn't tell me what I need to know any longer. Thus I added a new Ignore Rep setting. Fortunately, it fit well with the current data structure and required minimal code changes.

There is a new Set Ignore Rep button in the Reputation window that will open a new Ignore Rep window (can also open with "/dtw ir"). In this window, all kindred groups will be automatically set to ignore and change disabled. Clicking on a new group will flag it for no longer being considered for reputation gains for the current character. This will exclude it from Rep-Only listings and from "Find top" selection. When the group code is listed for a trophy, it will be colored magenta (instead of red for kindred) to flag it as a special case. Hopefully, I'm not the only one that will find this feature useful.

Of course the game's down now, so I can't verify which item, but I noticed last night that one of the Wilderfolk items wasn't being categorized correctly. Looking now at DT_data.lua, I see a bunch of entries for "Stone-warn Fur."
That's not a thing.
There is "Stone-worn Fur" so that might be what it's tripping up on?

Would just correcting the spelling on DT_data.lua fix this, if it is the case?

---EDIT---

Confirmed - Stone-Worn Fur is the item that wasn't categorized correctly, and a find-and-replace in DT_data.lua fixes it.

If anyone wants to fix this on their own, make sure to use a text editor that doesn't munge up file encoding, e.g. Notepad++, not Windows' built-in Notepad program.

Hmm.. I don't know what I'm doing wrong but I click the Download button and get 4.5.2.

I renamed the zip file to 4.6 (so it doesn't save over the actual copy of 4.5.2 I downloaded the other day) and comparing the contents of both zip files, they seem to be identical. Same date/time stamps and same CRC values.